1

Control of a Direct Matrix Converter withModulated Model Predictive Control

Abstract—This paper investigates the use of a model- predic-tive control strategy to control a direct matrix converter. Theproposed control method combines the features of the classicalModel Predictive Control and the Space Vector Modulationtechnique into a Modulated Model Predictive Control. This newsolution maintains all the characteristics of Model PredictiveControl (such as fast transient response ,multi-objective controlusing only one feedback loop, easy inclusion of non-linearitiesand constraints of the system, the flexibility to include othersystem requirements in the controller) adding the advantages ofworking at fixed switching frequency and improving the qualityof the controlled waveforms. Simulation and experimental resultsemploying the control method to a direct matrix converter arepresented.

Index Terms—Matrix Converter, Model Predictive Control,Modulated Model Predictive Control.

I. INTRODUCTION

A direct matrix converter(MC) is a AC/AC converter that iscapable of converting varying amplitude, fixed frequency inputto varying amplitude and frequency output without employingan intermediate DC-link capacitor. Nine bidirectional voltage-blocking current-conducting switches arranged in the form of amatrix as shown in Fig. 1 constitutes a MC making it possiblefor bidirectional power flow. In the recent years, MCs havereached a good level of technological maturity that allowstheir practical and industrial implementation in a variety ofapplications, such as industrial drives [1-2], power supplies[3], aerospace applications [4-7]. MC is often known as anall silicon converter as there are no bulky and heavy energystorage devices [8].

The first matrix converter modulation strategy was proposedby Alesina and Venturini [9]. Even though the initial strategyproposed was capable of producing sinusoidal input and outputwaveforms, the maximum voltage ratio it could achieve wasonly 0.5. Later several other modulation techniques whichproduce a higher voltage transfer ratio of 0.866 such asOptimum Venturini Modulation and Space Vector Modulation(SVM) were proposed later and SVM became the most widelyused modulation method for MC [10]. Since then, SVMhas been applied in many applications in conjunction withfeedback control strategies in order to regulate specific controlvariables[11].

Model Predictive Control (MPC), introduced in the lateseventies [12] considers a model of the system in orderto predict its future behaviour over a time horizon. A costfunction represents the desired behaviour of the system. MPCis an optimization problem where a sequence of future ac-tuations is obtained by minimizing the cost function. It isalso referred to as a receding horizon control, which meansthat at each instant the horizon is moved forward, the first

VA

VB

VC

Matrix Converter

IA

IB

IC

Vabc

Load

Bidirectional

switch

SAa

SBa

SCa

SAb

SBb

SCb

SAc

SBc

SCc

Input

Filter

Fig. 1. Schematic of a direct matrix converter system

element of the sequence calculated at each step is applied atthat instant and all the calculation is repeated every sampleperiod [13]. Due to the high sampling rate used in the controlof power converters, solving the optimization problem ofMPC online is not practical. One approach is to use anexplicit solution of MPC, solving the optimization problemoffline. The resulting controller is a lookup table and can beimplemented without big computational effort. Consideringthat power converters are systems with a finite number ofstates, given by the possible combinations of the state ofthe switching devices, the MPC optimization problem can besimplified and reduced to the prediction of the behaviour ofthe system for each possible state. Then, each prediction isevaluated using the cost function and the state that minimizesit, is selected. This approach has been successfully applied inrecent years for the control of power converters and drives,like for current control and power control for three phaseVoltage Sourse Inverters [13-14] and for current and torquecontrol for induction motor and permanent magnet motordrives[15-17]. Even though control of currents, torque andflux are achieved, the switching frequency is variable and notfixed. MPC presents several advantages, such as fast dynamicresponse, easy inclusion of nonlinearities and constraints ofthe system, flexibility to include other system requirements inthe controller, easy tuning of the control if the system modelis known and the possibility of modifying and extending themethodology depending on specific applications.

One of the interesting features of MPC is that due tothe absence of a modulator, the control chooses and appliesone converter switching state for the entire sampling instant.This generates large ripples in the waveforms resulting invariable and high switching frequencies compared to othercontrol methods. Various methods have been proposed in theliterature to improve the applied vector sequence [18] or to

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introduce a modulation scheme inside the MPC algorithm [19].However these methods involve complicated expressions forthe switching time patterns and are not flexible enough toinclude other system requirements in the cost function. Thisis overcome by modulated model predictive control (M2PC)which has been proposed for a cascaded H-bridge converter[20-22], active front-end rectifier [23], two level inverter [24],three phase rectifier [25], a neutral point clamp converter [26]and indirect matrix converter [27]. Inspired from this newapproach, [28] elaborates the application of M2PC for a directmatrix converter and includes experimental results to validatethe simulation results discussed in [29]. This paper includesa comparison of the performance of M2PC with conventionalcontrol methods such as MPC and Proportional-Integral (PI)controller.

II. SYSTEM MODEL

In order to design the control system, an accurate modelis required. The model description can be divided into matrixconverter model and load model as presented in the followingsubsections.

A. Matrix converter model

The voltages at the output of a matrix converter and inputcurrents are calculated from the input voltages and outputcurrents respectively and can be derived directly from Fig.1. The voltages and currents are represented in terms of theswitching functions related to each bidirectional switch in thematrix converter as shown in equations (1) and (2).

va(t)vb(t)vc(t)

=

SAa(t) SBa(t) SCa(t)SAb(t) SBb(t) SCb(t)SAc(t) SBc(t) SCc(t)

.vA(t)vB(t)vC(t)

(1)

iA(t)iB(t)iC(t)

=

SAa(t) SBa(t) SCa(t)SAb(t) SBb(t) SCb(t)SAc(t) SBc(t) SCc(t)

T

.

ia(t)ib(t)ic(t)

(2)

where ia(t), ib(t) and ic(t) are the output currents,iA(t), iB(t) and iC(t) the input currents, va(t), vb(t) and vc(t)the output voltages and vA(t), vB(t) and vC(t) the sourcevoltages and Sij(t) is the switching function for i= A,B andC and j= a,b and c.

B. Load model

To determine the load current in the next sampling interval,a mathematical model of the load is required. Matrix con-verters are usually connected to an inductive load and hencethis paper considers the model of a RL load to demonstrateM2PC. If M2PC needs to be implemented for MC feedingother loads such as an induction machine or a capacitive load,the load model needs to be derived appropriately. It is vitalto the performance of the controller that the load model isaccurate.

The continuous time model of a resistive-inductive load isgiven by equation (3).

Ldio(t)

dt= vo(t)−R io(t) (3)

where R and L are the load resistance and inductancerespectively,io(t) = [ia(t) ib(t) ic(t)]

T the load currents andvo(t) = [va(t) vb(t) vc(t)]

T the matrix converter output volt-age.

Discretising equation (3), using forward Euler approxima-tion, the discrete time model of the load can be obtained asshown in equation (4).

Io(k + 1) = (1− RTsL

)Io(k) +TsLVo(k) (4)

Equation (4) is then used to predict the load currents atthe future sampling instants in order to formulate the costfunctions.

III. MODULATED MODEL PREDICTIVE CONTROL FORDIRECT MATRIX CONVERTER

The M2PC strategy aims to combine the positive featuresof both SVM and MPC to obtain a model predictive controlbased algorithm with an intrinsic modulation scheme. A basiccontrol block diagram of the proposed strategy for a directmatrix converter is given in Fig. 2.

Optimization of Constraints

Load

Sij

Duty cycle

Matrix

Prediction of

Io (k+2)

Cost function

Current reference,

Iref

G0-4

/ abc

Load currents, Io

Converter voltage, Vc

Vc

Io

/ abc

t0-4

load currents estimation calculation

switching sequence

Converter

model

Fig. 2. Control block diagram for M2PC strategy

A reference current is imposed upon the system and thecontroller is designed using the system model so that the loadcurrent tracks the reference. The measured currents are thenused to predict the value of current at (k+1). The referenceand predicted currents are then used to calculate the costfunction which in turn is used to derive the duty cycles forthe selected voltage vectors. Unlike 2-level inverters with twoactive and three zero vectors, matrix converter usually makesuse of four active and three zero vectors to obtain sinusoidalwaveforms. Active vectors are those vectors that produce anon zero voltage. Zero vectors as the name suggests does notproduce any voltage.

The M2PC utilizes the SVM vector sequence and calculatesthe duty cycles for each voltage vector based on the mini-mization of the cost function. Fixed switching frequency is

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ensured in this case as the sequence of the vectors chosen bythe control will be applied within one sampling interval. Thedifference between a classical MPC and the M2PC is in theapplication time of the vectors. Unlike MPC where one vectoris applied for the whole sampling interval, in the M2PC ateach sampling interval; four active and three zero vectors areselected by the cost function minimization algorithm and areapplied for their respective duty cycles. The active and zerovectors are then arranged in a symmetrical manner as shownin Fig. 3; to achieve minimum switching losses and reduceharmonics. The switching pattern is similar to that used ina standard SVM scheme. t01, t02 and t03 are the applicationtimes for the three zero vectors and t1, t2, t3 and t4 for thefour active vectors.

Ts

V1z3 z1 z2 z1 z3

2

t01

2

t2

2

t1

2

t3t4

2t02

t4

2

t3

2

t01

2

t2

2

t1

2

t03

2

t03

2

V3V3 V4V2 V4 V2 V1

Fig. 3. Symmetrical switching pattern for a direct matrix converter

Fig. 4 shows the flowchart of M2PC algorithm incorporatingdelay compensation for the computation.

Fig. 4. Flowchart showing the M2PC algorithm

A. Prediction of Control Variables and Cost function calcula-tion

Similar to the MPC, the switching states are calculatedbased on a cost function minimization. The cost function caninclude different performance factors according to the controlvariables and to the constraints required. More than one vari-able can be controlled with the same control loop, providing

a multi-objective control approach and avoiding nested loops.In this paper, the M2PC algorithm is provisionally applied toa direct matrix converter feeding a RL load to demonstratecurrent control capability.

For an RL load, the prediction of load current makes useof the current measurement at the present instant or instant’k’ and the load parameters as shown in (4). For MPC, theprediction of load current is carried out once using the optimalswitching state from the previous instant. Since the M2PCincorporates a modulation scheme, more than one active vectorwill be applied during one sampling interval. For a directmatrix converter, out of the 27 switching states, the six rotatingvectors are not considered for modulation resulting in 21switching states to choose from. As in a standard SVM strategy[10] it is assumed that a minimum of four active vectors isrequired to get sinusoidal waveforms for a matrix converter.Hence the M2PC strategy will also consider four active vectorsand three zero vectors to apply during one sampling interval.The predictions for four active vectors and zero vectors aredone as if they were applied for the whole sampling interval.For example, for one sequence containing four active and threezero vectors, the predictions of load current are calculated asshown in equations (5) and (6). The predicted value of loadcurrent for the three zero vectors will be the same and henceit is only required to calculate once.

For active vectors :

Iio(k + 1) = (1− RTsL

)Iio(k) +TsLV io (k) (5)

for i=1,2,..4.For zero vectors:

Io(k + 1) = (1− RTsL

)Io(k) (6)

Once the currents at (k+1) instant are predicted, (k+2)predictions can be made by substituting Io(k) with Io(k+1)inequations (5) and (6).

Just as in MPC, the switching states are selected based ona cost function minimization. The cost function can includedifferent performance factors according to the control variablesand constraints required. More than one variable can becontrolled with the same control loop, providing a multi-objective control approach and avoiding nested loops.

The cost function for load current control is essentially theerror between the current demand and predicted current at(k+2) instant if the computation delay is compensated. Thisresults in five cost functions G0, G1, G2, G3 and G4 for eachactive and zero vectors. The set of quadratic cost functionscan be calculated using the pre-calculated predicted currentsin equation (5) as shown in (7).

Gi = (Ioref (k + 2)− Iio(k + 2))2 (7)

for i=0,1,...4.where Ioref (k + 2) is the current demand at (k+1) instant.The final cost function used for the minimization algorithm

constitutes the cost functions for the active and zero vectorsand is expressed as shown in equation (8). The minimization

4

algorithm is run for 18 combinations of active and zero vectorsequences.

G(final) = G1d1 +G2d2 +G3d3 +G4d4 +G0d0 (8)

where d0, d1, d2, d3 and d4 are the duty cycles for the voltagevectors.

Once the cost functions for each of the active and zero vec-tors are calculated; the predictive control will choose the bestsequence of vectors which produces the lowest error. Thesevectors are then applied within the sampling interval with theirrespective duty cycles. The duty cycles are calculated basedon the cost functions values of the active and zero vectors.

The multi-objective control capability of the M2PC can beachieved by simply adding the control variables to the costfunction for each vector and by specifying a weighting factorfor each of them. In this manner, it is possible to also considercertain constraints for the optimal operation of the system.This is demonstrated in [30] by controlling the stator currentsand input reactive power of an induction motor fed by a directmatrix converter without the use of nested loops.

B. Calculation of Duty Cycles

The application times for each of the vectors are calculatedfrom the cost functions computed for each the switching state.This method is based on the assumption that per samplinginterval, the system behavior is linear in nature. From this itis possible to derive the application times for each vector asa percentage of the total sampling time. The relation betweenthe application times of the vectors and their correspondingcost functions can be written as follows.

t =k1G

(9)

where k1 is the proportional constant and G is the costfunction. Using the above equation for four active vectors andzero vector for a MC will result in a set of five equations, eachdictating the application times for a particular vector in termsof the proportional constant. The condition that holds true forall the vectors applied is that the sum of the application timesfor all the vectors should be equal to the sampling time asshown in (10).

t1 + t2 + t3 + t4 + t0 = Ts (10)

where t1, t2, t3, t4 are the times for the four active vectors andt0 is the time for three zero vectors. By substituting equation(9) in (10), the proportional constant can be obtained as shownin (11).

k1 =G0G1G2G3G4Ts

A(11)

where A = (G1G2G3G4 +G0G2G3G4 +G0G1G3G4 +G0G1G2G4 +G0G1G2G3).

The application times for the vectors can then be derivedby substituting the value of the proportional constant. Theresulting set of duty cycles is shown in equation (12).

t1 =(G0G2G3G4Ts)

A

t2 =(G0G1G3G4Ts)

A

t3 =(G0G1G2G4Ts)

A

t4 =(G0G1G2G3Ts)

A

(12)

Once the application times for active vectors are obtained,the time for zero vectors can be calculated from equation (10).

t0 = Ts − (t1 + t2 + t3 + t4) (13)

The duty cycles for each of the vector will be related to theerror associated with that voltage vector. The direct relationof the duty cycles with the cost functions makes this methodunique. The active and zero vectors are then applied for theirrespective duty cycles within one sampling interval.

The active and zero vectors are then arranged in a symmetri-cal manner as shown in Fig. 3; to achieve minimum switchinglosses and reduced harmonics. The switching pattern is similarto that used in a SVM scheme. t01, t02 and t03 are the appli-cation times for the three zero vectors and t1, t2, t3 and t4 forthe four active vectors in Fig. 3.

The switching frequency that can be attained using thismethod depends on the computational speed of the micro-processor being used. The matrix converter requires a sig-nificant computational overhead for this method since 27switching states are available. The maximum controller updatefrequency obtained for M2PC within the laboratory whenusing a Texas Instruments C6713 DSP was 20kHz.

IV. SIMULATION RESULTS

The M2PC is applied to a direct matrix converter feedingan RL load and simulations are done in Matlab Simulinkenvironment to study its performance. A sampling time of80µs is considered. The simulation also takes into account thefour-step commutation in matrix converter and the measure-ment delays in the control platform. An LC input filter with adamping resistor is employed to mitigate the high frequencycomponents of the input current of the matrix converter. Acontrol block diagram showing the different steps involvedin the load current control of a direct matrix converter usingM2PC is shown in Fig. 5.

5

VA

VB

VC

Matrix

Converter

IA

IB

IC

Va

Vb

Vc

Load

abc to

Duty cycle calculation

Cost function

minimization

Input

filter

Prediction of

load currents

Sij

Iref

Io(k+1)

Io

Fig. 5. Control block diagram of M2PC for a matrix converter

The system parameters for both the simulation and experi-mental tests are given in Table. I.

TABLE ISYSTEM PARAMETERS

Parameter Value Unit

Filter inductance 0.7 mH

Filter capacitance (delta) 8.3 µF

Damping resistor 15 Ω

Load resistance 10 Ω

Load inductance 3.75 mH

Sampling time 80 µs

The load current of a matrix converter feeding an RL load iscontrolled using M2PC and the resulting waveforms are shownbelow. A load current reference of 5A at 30Hz is demandedfrom the system. Fig. 6 shows the controlled three phase loadcurrents, MC line voltage at steady state and the Fast FourierTransform (FFT) of the load current at steady state. It is worthnoting the presence of harmonics in the range of switchingfrequency, 12.5kHz and its multiples. This is a result of fixedswitching frequency operation. To analyse the quality of thecontrolled waveforms the Total Harmonic Distortion (THD) ofPhase A load current is calculated and is approximately 6.3%.

0 0.02 0.04 0.06 0.08 0.1

−505

Thr

ee p

h lo

ad c

urre

nts(

A)

0 0.02 0.04 0.06 0.08 0.1−200

0

200

Time (s)

MC

Out

put

line

vol

tage

(V

)

0 0.5 1 1.5 2 2.5 3

x 104

00.10.2

Frequency(Hz)

Mag

nitu

de(A

)

Phase aPhase bPhase c

Fig. 6. Three phase load currents of MC controlled by M2PC

To demonstrate the fast dynamic response of M2PC, a stepchange from 2A to 4A and then to 2A. The resulting waveformis shown in Fig. 7 (top).

0 0.05 0.1 0.15 0.2 0.25 0.3

−5

0

5

Alp

ha−

beta

load

cur

rent

s (A

)

0 0.05 0.1 0.15 0.2 0.25 0.3

−5

0

5

Alp

ha−

beta

lo

ad c

urre

nts

(A)

Time (s)

Ialpha

Ibeta

Irefalpha

Irefbeta

Ialpha

Ibeta

Irefalpha

Irefbeta

Fig. 7. Alpha-beta currents when the frequency of reference is changed

It is evident from the figure that the load current im-mediately follows the step demand in reference current andreaches steady state immediately. This indicates that M2PCcan provide fast transient response which is a characteristic itinherited from MPC. In addition to the step change in currentreference magnitude, a step change in the frequency of thecurrent reference from 20Hz to 40Hz is also introduced.Theresulting waveform is shown in Fig. 7 (bottom). The resultsindicate that M2PC is able to handle any abrupt changes inthe reference signal without any overshoots or instability.

In order to conduct a quantitative analysis of the transient

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response of the M2PC controller, load current control of matrixconverter is implemented using MPC and a conventionalPI Controller. The system parameters for the three methodsremain constant. A step demand in load current amplitudefrom 2A to 4A is applied to the controller and the resultingd-axis load currents with the reference signal for all the threecontrol methods is shown in Fig. 8. To conduct a fair analysisof the transient response of the controllers considered, thePI controller is tuned to achieve very fast response to set abenchmark for the comparison.

The simulation results for load current control of a directMC with RL load are considered to compare the performanceof M2PC controller with PI Controller and MPC. The THD ofthe currents controlled by the three methods can be consideredas a measure of their steady state performance. To analyse thetransient performance of the control strategies, the rise timeof the controlled currents during a step change is considered.Rise time is the time taken by the control variable to reachfrom 10% to 90% of the steady state value. A comparison ofthe THDs and rise times for load current control of a MC fordifferent controllers such as PI controller, MPC and M2PCfrom simulation results is tabulated in Table. II.

0.04 0.045 0.05 0.055 0.06 0.06502468

0.04 0.045 0.05 0.055 0.06 0.06502468

d−ax

is lo

ad c

urre

nt (

A)

0.04 0.045 0.05 0.055 0.06 0.06502468

Time (s)

Idref

IdM2PC

MPC

PI Controller

Fig. 8. d-axis load current with reference during a step change in theamplitude

TABLE IICOMPARISON OF THDS AND RISE TIMES OF LOAD CURRENTS FOR

DIFFERENT CONTROL STRATEGIES

Control Strategy Steady State Transient Performance

Performance(THD) (Risetime)

PI Controller 1.89% 4.1ms

MPC 8.09% 0.34ms

M2PC 6.3% 0.65ms

From Table. II it can be seen that PI Controller with SVM

resulted in waveforms with least harmonic distortion followedby M2PC. MPC resulted in waveforms with the worst currentquality. Predictive control based algorithms such as MPC andM2PC had faster dynamic response with rise times of 0.34msand 0.65ms respectively; compared to that of PI controllerthat resulted in a rise time of 4.1ms. These results prove thatM2PC is capable of fast dynamic response very similar tothat of MPC when compared to a traditional PI controller anddeliver waveforms with enhanced current quality compared toMPC.

V. EXPERIMENTAL RESULTS

To validate the simulation results discussed in the previoussection, the M2PC is implemented on a matrix converterfeeding an RL load in the laboratory. The parameters of thesystem are given in Table. I.

Fig. 9. Experimental setup

The experimental setup shown in Fig. 9 includes a matrixconverter using SK60GM123 IGBT modules rated at 1200Vand 60A, a current direction detection circuit for four stepcommutation and a clamp circuit for over voltage protection.Each IGBT module consists of two diodes and two anti-parallel IGBT connected in the common emitter configuration.There are three current sensors to measure the output currentsand three voltage sensors to measure the supply voltage tothe converter. The control platform includes a Texas instru-ment DSP and a FPGA card developed at Power ElectronicsMachines and Control (PEMC) Group, The University OfNottingham. The M2PC algorithm is implemented on the DSPat a sampling frequency of 80µ s. An FPGA interface with theDSP ensures the four-step commutation of the switches. Thesetup is powered using Chroma Programmable AC source asindicated in Fig. 9.

The load currents of the direct matrix converter are con-trolled using the M2PC strategy. A reference current of 5Aat 30Hz is demanded from the system and the experimentalresults of controlled load currents, MC output line voltage andthe harmonic spectrum of Phase A load current are shownin Fig. 10. It is evident from Fig. 10 that the load currentsare sinusoidal and reaches the steady state value without anyerror. The THD of the controlled waveforms is approximately

7

10.8%. The harmonic spectrum of Phase A load current revealsharmonics in the range of switching frequency (12.5kHz)and its multiples which confirms fixed switching frequencyoperation. This validates the simulation results shown in Fig.6.

0 0.02 0.04 0.06 0.08 0.1

−505

Thr

ee p

hase

load

cur

rent

s(A

)

0 0.02 0.04 0.06 0.08 0.1−200

0

200

Time (s)

MC

Out

put

line

volta

ge (

V)

0 0.5 1 1.5 2 2.5 3

x 104

0

0.1

Frequency(Hz)

Mag

nitu

de(A

)

Phase aPhase bPhase c

Fig. 10. Phase A load current, MC output line voltage and harmonic spectrumof load current at steady state

To analyse the transient behavior of the control strategy, astep demand in the amplitude and frequency of the referencecurrent waveform is applied. A step in the amplitude ofreference current waveform from 2A to 4A is applied andthe frequency of the reference load current is changed from20Hz to 40Hz and the resulting waveforms are shown in Fig.11.

0 0.05 0.1 0.15 0.2

-5

0

5

Thr

ee p

hase

load

cur

rent

s(A

)

Phase aPhase bPhase c

0.1 0.2 0.3 0.4 0.5Time (s)

-5

0

5

Alp

ha-b

eta

load

cur

rent

s (A

)

Irefalpha

Ialpha

Irefbeta

Ibeta

Fig. 11. Dynamic performance of M2PC during step change in the magni-tude(top) and frequency(bottom) of the reference load current

From Fig. 11, it is evident that the load currents respondto the sudden changes in amplitude and frequency instanta-neously without any delay. The results from the experimental

tests conforms to the simulation results which proves thesystem model and control strategy. To summarize, the loadcurrent control achieved by this method is characterized byvery fast transient response as in the case of MPC and animproved steady state response due to the presence of aninbuilt modulation scheme.

VI. EFFECT OF SAMPLING TIME ON WAVEFORM QUALITY

Since the performance of MPC is largely dependant onthe sampling interval, it is worth studying if this applies tothe M2PC. For MPC, quality of the controlled currents areimproved as the sampling interval gets smaller. To analysethe effect of sampling time on the quality of the controlledwaveforms in this case the load currents, the M2PC strategyis implemented for three different sampling times such as50µs, 80µs and 100µs. The quality of the controlled currentsare assessed by comparing the THDs for these sampling times.Both simulation and experimental tests are conducted for threedifferent sampling intervals or switching frequencies and theTHDs of the resulting current waveforms are tabulated asshown in Table. III.

TABLE IIICOMPARISON OF THDS FOR M2PC WITH DIFFERENT SAMPLING

INTERVALS

Sampling time Total Harmonic DistortionSimulationResults Experimental Results

50µs 4.0% 7.33%

80µs 6.3% 10.8%

100µs 7.5% 12.07%

Table. III indicates that there is a considerable effect on thequality of the controlled waveforms as the sampling intervalis changed. The current quality was the best when a samplingtime of 50µs is considered and the worst when the samplingtime is 100µs. It is interesting to note that the M2PC strategyis also dependant on the sampling interval considered whichis expected as it is predominantly a predictive control basedmethod.

VII. CONCLUSION

A control method with the features of MPC and a mod-ulation scheme similar to SVM is proposed in this paperfor a direct matrix converter drives. The ability to controldifferent parameters simultaneously, high controller bandwidthand constant switching frequency are the main highlights ofthis method. The constant switching behavior of the SVMutilised in this method guarantees that a predictive basedcontrol method can now be used where the traditional associ-ated problems with input filter sizing, harmonic performance,switching loss and hence thermal management design can nowbe addressed in a more predictable and systematic way. Acomparison of the performance of M2PC with control methodssuch as MPC and PI controller showed that M2PC is capableof fast dynamic response. The experimental results presentedin this paper validates the M2PC strategy for load currentcontrol of a direct matrix converter.

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VIII. REFERENCES

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[2] P. W. Wheeler, J. C. Clare, D. Katsis, L. Empringham,M. Bland and T. Podlesak, ”Design and constructionof a 150 KVA matrix converter induction motor drive,”Power Electronics, Machines and Drives, 2004. (PEMD2004). Second International Conference on (Conf. Publ.No. 498), Edinburgh, UK, 2004, pp. 719-723 Vol.2.

[3] P. Zanchetta, P. W. Wheeler, J. C. Clare, M. Bland, L.Empringham and D. Katsis, ”Control Design of a Three-Phase Matrix-Converter-Based ACAC Mobile UtilityPower Supply,” in IEEE Transactions on Industrial Elec-tronics, vol. 55, no. 1, pp. 209-217, Jan. 2008.

[4] L. Empringham, J. W. Kolar, J. Rodriguez, P. W.Wheeler, and J. C. Clare, ”Technological Issues andIndustrial Application of Matrix Converters: A Review,”IEEE Transactions on Industrial Electronics, vol. 60, pp.4260-4271, 2013.

[5] L. de Lillo, L. Empringham, P. Wheeler, J. Clare and K.Bradley, ”A 20 KW matrix converter drive system foran electro-mechanical aircraft (EMA) actuator,” PowerElectronics and Applications, 2005 European Confer-ence on, Dresden, 2005, pp. 6 pp.-P.6.

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